Understandable; perhaps. In mathematics, it is very easy to say understandable things that are simply false. In this case, those false things become nonsense when you realize that the meaning of “parallel lines” is “lines that do not intersect”.
You might say that an explanation gets these facts completely wrong, then it is still a good explanation if it makes you think the right things. I say that such an explanation goes against the spirit of all mathematics. It is not enough that your argument is understandable, for many understandable arguments have later turned out to be incoherent. It is not enough that your argument is believable, for many believable arguments have later turned out to be false.
If you want to do good mathematics, the statements you make must be true.
Understandable; perhaps. In mathematics, it is very easy to say understandable things that are simply false. In this case, those false things become nonsense when you realize that the meaning of “parallel lines” is “lines that do not intersect”.
You might say that an explanation gets these facts completely wrong, then it is still a good explanation if it makes you think the right things. I say that such an explanation goes against the spirit of all mathematics. It is not enough that your argument is understandable, for many understandable arguments have later turned out to be incoherent. It is not enough that your argument is believable, for many believable arguments have later turned out to be false.
If you want to do good mathematics, the statements you make must be true.